SOLUTION: Solve the problem using rules of inference and replacement: Premise 1) Q v (R . S) Premise 2) (Q > T) . (T > S) Conclusion /:S

Algebra.Com
Question 1038513: Solve the problem using rules of inference and replacement:
Premise 1) Q v (R . S)
Premise 2) (Q > T) . (T > S)
Conclusion /:S
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


    1:   Q or (R and S)
    2:   (Q -> T) and (T -> S)    |    S
    3:   Assume Q
         4:  Q -> T               2    Conjunction Elimination
         5:  T                    3,4  Modus Ponens
         6:  T -> S               2    Conjunction Elimination
         7:  S                    5,6  Modus Ponens

    8:   Assume ~Q
         9:  R and S              1,8  Disjunctive Syllogism
        10:  S                    9    Conjunction Elimination

   11:   :. S                     3-7,8-10 Law of Excluded Middle

John

My calculator said it, I believe it, that settles it
RELATED QUESTIONS

Using Inference Rules Premise 1. (P * Q) > R Premise 2. (P * Q) V S Premise 3. ~ R (answered by Edwin McCravy)
Can you please assist me with these problems? We are using the Rules of Inference and the (answered by jim_thompson5910)
Construct deductions for each of the following arguments using Group I rules. (1) 1.... (answered by math_helper)
Prove using Inference and Replacement Rules: 1). Q -> R 2). R -> S 3). ~S... (answered by math_tutor2020)
Construct proofs using the Rules of Inference and the Rules of Replacement. The... (answered by jim_thompson5910)
1. T ⊃ (Q & F) 2. T & C/Q v O I am trying to solve this equation using the... (answered by math_tutor2020)
use the inference rules, replacement rules, indirect proof and/or conditional proof to... (answered by mccravyedwin,Edwin McCravy)
premise (P&Q)V(R&S) Premise R->L goal... (answered by Edwin McCravy)
Construct proofs using the Rules of Inference and the Rules of Replacement. The... (answered by jim_thompson5910)